1. 4 Forecasting PowerPoint presentation to accompany Heizer and Render
Operations Management, Eleventh Edition
Principles of Operations Management, Ninth Edition
PowerPoint slides by Jeff Heyl
© 2014 Pearson Education, Inc.

2. Outline What Is Forecasting? The Strategic Importance of Forecasting
Seven Steps in the Forecasting System
Forecasting Approaches

3. Outline - Continued Time-Series Forecasting
Associative Forecasting Methods: Regression and Correlation Analysis
Monitoring and Controlling Forecasts
Forecasting in the Service Sector

4. Learning Objectives
When you complete this chapter you should be able to :
Understand the three time horizons and which models apply for each use
Explain when to use each of the four qualitative models
Apply the naive, moving average, exponential smoothing, and trend methods

5. Learning Objectives
When you complete this chapter you should be able to :
Compute three measures of forecast accuracy
Develop seasonal indices
Conduct a regression and correlation analysis
Use a tracking signal

6. ?? What is Forecasting? Process of predicting a future event
Underlying basis of all business decisions
Production
Inventory
Personnel
Facilities ??

7. Forecasting Time Horizons
Short-range forecast
Up to 1 year, generally less than 3 months
Purchasing, job scheduling, workforce levels, job assignments, production levels
Medium-range forecast
3 months to 3 years
Sales and production planning, budgeting
Long-range forecast
3+ years
New product planning, facility location, research and development

8. Distinguishing Differences
Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes
Short-term forecasting usually employs different methodologies than longer-term forecasting
Short-term forecasts tend to be more accurate than longer-term forecasts

9. Influence of Product Life Cycle
Introduction – Growth – Maturity – Decline
Introduction and growth require longer forecasts than maturity and decline
As product passes through life cycle, forecasts are useful in projecting
Staffing levels
Inventory levels
Factory capacity

10. Types of Forecasts Economic forecasts Technological forecasts
Address business cycle – inflation rate, money supply, housing starts, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing products and services

11. Seven Steps in Forecasting
Determine the use of the forecast
Select the items to be forecasted
Determine the time horizon of the forecast
Select the forecasting model(s)
Gather the data needed to make the forecast
Make the forecast
Validate and implement results

12. The Realities!
Forecasts are seldom perfect, unpredictable outside factors may impact the forecast
Most techniques assume an underlying stability in the system
Product family and aggregated forecasts are more accurate than individual product forecasts

13. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting sales on Internet

14. Forecasting Approaches
Quantitative Methods
Used when situation is ‘stable’ and historical data exist
Existing products
Current technology
Involves mathematical techniques
e.g., forecasting sales of color televisions

15. Overview of Qualitative Methods
Jury of executive opinion
Pool opinions of high-level experts, sometimes augment by statistical models
Delphi method
Panel of experts, queried iteratively

16. Overview of Qualitative Methods
Sales force composite
Estimates from individual salespersons are reviewed for reasonableness, then aggregated
Market Survey
Ask the customer

17. Jury of Executive Opinion
Involves small group of high-level experts and managers
Group estimates demand by working together
Combines managerial experience with statistical models
Relatively quick
‘Group-think’ disadvantage

18. (Evaluate responses and make decisions)
Delphi Method
Iterative group process, continues until consensus is reached
3 types of participants
Decision makers
Staff
Respondents
Decision Makers
(Evaluate responses and make decisions)
Staff
(Administering survey)
Respondents
(People who can make valuable judgments)

19. Sales Force Composite Each salesperson projects his or her sales
Combined at district and national levels
Sales reps know customers’ wants
May be overly optimistic

20. Market Survey Ask customers about purchasing plans
Useful for demand and product design and planning
What consumers say, and what they actually do may be different
May be overly optimistic

21. Overview of Quantitative Approaches
Naive approach
Moving averages
Exponential smoothing
Trend projection
Linear regression
Time-series models
Associative model

22. Time-Series Forecasting
Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values, no other variables important
Assumes that factors influencing past and present will continue influence in future

23. Time-Series Components
Trend
Cyclical
Seasonal
Random

24. Average demand over 4 years
Components of Demand
Trend component
Demand for product or service
| | | |
Time (years)
Seasonal peaks
Actual demand line
Average demand over 4 years
Random variation
Figure 4.1

25. Trend Component Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc.
Typically several years duration

26. NUMBER OF “SEASONS” IN PATTERN
Seasonal Component
Regular pattern of up and down fluctuations
Due to weather, customs, etc.
Occurs within a single year
PERIOD LENGTH
“SEASON” LENGTH
NUMBER OF “SEASONS” IN PATTERN
Week
Day 7
Month
4 – 4.5
28 – 31
Year
Quarter 4 12 52

27. Cyclical Component Repeating up and down movements
Affected by business cycle, political, and economic factors
Multiple years duration
Often causal or associative relationships

28. Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Short duration and nonrepeating
M T W T F

29. Naive Approach
Assumes demand in next period is the same as demand in most recent period
e.g., If January sales were 68, then February sales will be 68
Sometimes cost effective and efficient
Can be good starting point

30. Moving Average Method MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time

31. Moving Average Example
MONTH
ACTUAL SHED SALES
3-MONTH MOVING AVERAGE
January 10
February 12
March 13
April 16
May 19
June 23
July 26
August 30
September 28
October 18
November
December 14 10 12 13
( )/3 = 11 2/3
( )/3 = 13 2/3
( )/3 = 16
( )/3 = 19 1/3
( )/3 = 22 2/3
( )/3 = 26 1/3
( )/3 = 28
( )/3 = 25 1/3
( )/3 = 20 2/3

32. Weighted Moving Average
Used when some trend might be present
Older data usually less important
Weights based on experience and intuition
Weighted moving average

33. Weighted Moving Average
MONTH
ACTUAL SHED SALES
3-MONTH WEIGHTED MOVING AVERAGE
January 10
February 12
March 13
April 16
May 19
June 23
July 26
August 30
September 28
October 18
November
December 14
[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6 10 12 13
WEIGHTS APPLIED
PERIOD 3
Last month 2
Two months ago 1
Three months ago 6
Sum of the weights
Forecast for this month =
3 x Sales last mo. + 2 x Sales 2 mos. ago + 1 x Sales 3 mos. ago

34. Weighted Moving Average
MONTH
ACTUAL SHED SALES
3-MONTH WEIGHTED MOVING AVERAGE
January 10
February 12
March 13
April 16
May 19
June 23
July 26
August 30
September 28
October 18
November
December 14 10 12 13
[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6
[(3 x 16) + (2 x 13) + (12)]/6 = 14 1/3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 20 1/2
[(3 x 26) + (2 x 23) + (19)]/6 = 23 5/6
[(3 x 30) + (2 x 26) + (23)]/6 = 27 1/2
[(3 x 28) + (2 x 30) + (26)]/6 = 28 1/3
[(3 x 18) + (2 x 28) + (30)]/6 = 23 1/3
[(3 x 16) + (2 x 18) + (28)]/6 = 18 2/3

35. Potential Problems With Moving Average
Increasing n smooths the forecast but makes it less sensitive to changes
Does not forecast trends well
Requires extensive historical data

36. Graph of Moving Averages
Weighted moving average
| | | | | | | | | | | |
J F M A M J J A S O N D
Sales demand
30 –
25 –
20 –
15 –
10 –
5 –
Month
Actual sales
Moving average
Figure 4.2

37. Exponential Smoothing
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Subjectively chosen
Involves little record keeping of past data

38. Exponential Smoothing
New forecast = Last period’s forecast
+ a (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + a(At – 1 - Ft – 1)
where Ft = new forecast
Ft – 1 = previous period’s forecast
a = smoothing (or weighting) constant (0 ≤ a ≤ 1)
At – 1 = previous period’s actual demand

39. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20

40. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142)

41. Exponential Smoothing Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant a = .20
New forecast = (153 – 142) =
= ≈ 144 cars

42. Effect of Smoothing Constants
Smoothing constant generally .05 ≤ a ≤ .50
As a increases, older values become less significant
WEIGHT ASSIGNED TO
SMOOTHING CONSTANT
MOST RECENT PERIOD
(a)
2ND MOST RECENT PERIOD
a(1 – a)
3RD MOST RECENT PERIOD
a(1 – a)2
4th MOST RECENT PERIOD
a(1 – a)3
5th MOST RECENT PERIOD
a(1 – a)4
a = .1 .1
.09
.081
.073
.066
a = .5 .5
.25
.125
.063
.031

43. Impact of Different  225 – 200 – 175 – 150 – Demand | | | | | | | | |
225 –
200 –
175 –
150 –
| | | | | | | | |
Quarter
Demand
Actual demand
a = .5
a = .1

44. Impact of Different 
225 –
200 –
175 –
150 –
| | | | | | | | |
Quarter
Demand
Choose high values of  when underlying average is likely to change
Choose low values of  when underlying average is stable
Actual demand
a = .5
a = .1

45. Choosing 
The objective is to obtain the most accurate forecast no matter the technique
We generally do this by selecting the model that gives us the lowest forecast error
Forecast error = Actual demand – Forecast value
= At – Ft

46. Common Measures of Error
Mean Absolute Deviation (MAD)

47. ACTUAL TONNAGE UNLOADED
Determining the MAD
QUARTER
ACTUAL TONNAGE UNLOADED
FORECAST WITH a = .10
FORECAST WITH
a = .50 1
180
175 2
168
= (180 – 175)
177.50 3
159
= (168 – )
172.75 4
= (159 – )
165.88 5
190
= (175 – )
170.44 6
205
= (190 – )
180.22 7
= (205 – )
192.61 8
182
= (180 – )
186.30 9 ?
= (182 – )
184.15

48. Determining the MAD QUARTER ACTUAL TONNAGE UNLOADED FORECAST WITH
ABSOLUTE DEVIATION FOR a = .10
a = .50
ABSOLUTE DEVIATION FOR a = .50 1
180
175
5.00 2
168
175.50
7.50
177.50
9.50 3
159
174.75
15.75
172.75
13.75 4
173.18
1.82
165.88
9.12 5
190
173.36
16.64
170.44
19.56 6
205
175.02
29.98
180.22
24.78 7
178.02
1.98
192.61
12.61 8
182
178.22
3.78
186.30
4.30
Sum of absolute deviations:
82.45
98.62
MAD =
Σ|Deviations|
10.31
12.33 n

49. Common Measures of Error
Mean Squared Error (MSE)

50. ACTUAL TONNAGE UNLOADED
Determining the MSE
QUARTER
ACTUAL TONNAGE UNLOADED
FORECAST FOR a = .10
(ERROR)2 1
180
175
52 = 25 2
168
175.50
(–7.5)2 = 56.25 3
159
174.75
(–15.75)2 = 4
173.18
(1.82)2 = 3.31 5
190
173.36
(16.64)2 = 6
205
175.02
(29.98)2 = 7
178.02
(1.98)2 = 3.92 8
182
178.22
(3.78)2 = 14.29
Sum of errors squared = 1,526.52

51. Common Measures of Error
Mean Absolute Percent Error (MAPE)

52. ACTUAL TONNAGE UNLOADED ABSOLUTE PERCENT ERROR
Determining the MAPE
QUARTER
ACTUAL TONNAGE UNLOADED
FORECAST FOR a = .10
ABSOLUTE PERCENT ERROR
100(ERROR/ACTUAL) 1
180
175.00
100(5/180) = 2.78% 2
168
175.50
100(7.5/168) = 4.46% 3
159
174.75
100(15.75/159) = 9.90% 4
175
173.18
100(1.82/175) = 1.05% 5
190
173.36
100(16.64/190) = 8.76% 6
205
175.02
100(29.98/205) = 14.62% 7
178.02
100(1.98/180) = 1.10% 8
182
178.22
100(3.78/182) = 2.08%
Sum of % errors = 44.75%

53. Comparison of Forecast Error
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50

54. Comparison of Forecast Error
MAD =
∑ |deviations| n
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 82.45/8 = 10.31
For a = .10
= 98.62/8 = 12.33
For a = .50

55. Comparison of Forecast Error
MSE =
∑ (forecast errors)2 n
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 1,526.54/8 =
For a = .10
MAD
= 1,561.91/8 =
For a = .50

56. Comparison of Forecast Error
MAPE =
∑100|deviationi|/actuali n
i = 1
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
= 44.75/8 = 5.59%
For a = .10
MAD
MSE
= 54.05/8 = 6.76%
For a = .50

57. Comparison of Forecast Error
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded a = .10 a = .10 a = .50 a = .50
MAD
MSE
MAPE 5.59% 6.76%

58. Trend Projections
Fitting a trend line to historical data points to project into the medium to long-range
Linear trends can be found using the least squares technique
y = a + bx ^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable ^

59. Least Squares Method Actual observation (y-value)
Time period
Values of Dependent Variable (y-values)
| | | | | | |
Deviation1
(error)
Deviation5
Deviation7
Deviation2
Deviation6
Deviation4
Deviation3
Actual observation (y-value)
Least squares method minimizes the sum of the squared errors (deviations)
Trend line, y = a + bx ^
Figure 4.4

60. Least Squares Method
Equations to calculate the regression variables

61. Least Squares Example YEAR ELECTRICAL POWER DEMAND 1 74 5 105 2 79 6
142 3 80 7
122 4 90

62. Least Squares Example YEAR (x) ELECTRICAL POWER DEMAND (y) x2 xy 1 7479 4
158 3 80 9
240 90 16
360 5
105 25
525 6
142 36
852 7
122 49
854
Σx = 28
Σy = 692
Σx2 = 140
Σxy = 3,063

63. Least Squares Example Demand in year 8 = 56.70 + 10.54(8)
YEAR (x)
ELECTRICAL POWER
DEMAND (y) x2 xy 1 74 2 79 4
158 3 80 9
240 90 16
360 5
105 25
525 6
142 36
852 7
122 49
854
Σx = 28
Σy = 692
Σx2 = 140
Σxy = 3,063
Demand in year 8 = (8)
= , or 141 megawatts

64. Least Squares Example Trend line, y = 56.70 + 10.54x 160 – 150 – 140 –^
| | | | | | | | |
160 –
150 –
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
60 –
50 –
Year
Power demand (megawatts)
Figure 4.5

65. Least Squares Requirements
We always plot the data to insure a linear relationship
We do not predict time periods far beyond the database
Deviations around the least squares line are assumed to be random

66. Seasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand

67. Seasonal Variations In Data
Steps in the process for monthly seasons:
Find average historical demand for each month
Compute the average demand over all months
Compute a seasonal index for each month
Estimate next year’s total demand
Divide this estimate of total demand by the number of months, then multiply it by the seasonal index for that month

68. Seasonal Index Example
DEMAND
MONTH
YEAR 1
YEAR 2
YEAR 3
AVERAGE YEARLY DEMAND
AVERAGE MONTHLY DEMAND
SEASONAL INDEX
Jan 80 85
105
Feb 70
Mar 93 82
Apr 90 95
115
May
113
125
131
June
110
120
July
100
102
Aug 88
Sept
Oct 77 78
Nov 75 83
Dec 90 80 85
100
123
115
105
Total average annual demand = 1,128

69. Seasonal Index Example
DEMAND
MONTH
YEAR 1
YEAR 2
YEAR 3
AVERAGE YEARLY DEMAND
AVERAGE MONTHLY DEMAND
SEASONAL INDEX
Jan 80 85
105 90 94
Feb 70
Mar 93 82
Apr 95
115
100
May
113
125
131
123
June
110
120
July
102
Aug 88
Sept
Oct 77 78
Nov 75 83
Dec
Total average annual demand =
1,128
Average monthly demand

70. Seasonal Index Example
DEMAND
MONTH
YEAR 1
YEAR 2
YEAR 3
AVERAGE YEARLY DEMAND
AVERAGE MONTHLY DEMAND
SEASONAL INDEX
Jan 80 85
105 90 94
Feb 70
Mar 93 82
Apr 95
115
100
May
113
125
131
123
June
110
120
July
102
Aug 88
Sept
Oct 77 78
Nov 75 83
Dec
Total average annual demand =
1,128
.957( = 90/94)
Seasonal index

71. Seasonal Index Example
DEMAND
MONTH
YEAR 1
YEAR 2
YEAR 3
AVERAGE YEARLY DEMAND
AVERAGE MONTHLY DEMAND
SEASONAL INDEX
Jan 80 85
105 90 94
.957( = 90/94)
Feb 70
.851( = 80/94)
Mar 93 82
.904( = 85/94)
Apr 95
115
100
1.064( = 100/94)
May
113
125
131
123
1.309( = 123/94)
June
110
120
1.223( = 115/94)
July
102
1.117( = 105/94)
Aug 88
Sept
Oct 77 78
Nov 75 83
Dec
Total average annual demand =
1,128

72. Seasonal Index Example
Seasonal forecast for Year 4
MONTH
DEMAND
Jan
1,200
x .957 = 96
July
x = 112 12
Feb
x .851 = 85
Aug
x = 106
Mar
x .904 = 90
Sept
Apr
Oct
May
x = 131
Nov
June
x = 122
Dec

73. Seasonal Index Example
Year 4 Forecast
Year 3 Demand
Year 2 Demand
Year 1 Demand
140 –
130 –
120 –
110 –
100 –
90 –
80 –
70 –
| | | | | | | | | | | |
J F M A M J J A S O N D
Time
Demand

74. San Diego Hospital Trend Data 10,200 – 10,000 – 9,800 – 9,600 –
Figure 4.6
10,200 –
10,000 –
9,800 –
9,600 –
9,400 –
9,200 –
9,000 –
| | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Month
Inpatient Days
9530
9551
9573
9594
9616
9637
9659
9680
9702
9724
9745
9766

75. San Diego Hospital
Seasonality Indices for Adult Inpatient Days at San Diego Hospital
MONTH
SEASONALITY INDEX
January
1.04
July
1.03
February
0.97
August
March
1.02
September
April
1.01
October
1.00
May
0.99
November
0.96
June
December
0.98

76. San Diego Hospital Seasonal Indices 1.06 – 1.04 – 1.04 1.02 – 1.03
Figure 4.7
1.06 –
1.04 –
1.02 –
1.00 –
0.98 –
0.96 –
0.94 –
0.92 –
| | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Month
Index for Inpatient Days
1.04
1.02
1.01
0.99
1.03
1.00
0.98
0.97
0.96

77. San Diego Hospital Period 67 68 69 70 71 72 Month Jan Feb Mar Apr May
June
Forecast with Trend & Seasonality
9,911
9,265
9,164
9,691
9,520
9,542 73 74 75 76 77 78
July
Aug
Sept
Oct
Nov
Dec
9,949
10,068
9,411
9,724
9,355
9,572

78. San Diego Hospital Combined Trend and Seasonal Forecast 10,200 –
Figure 4.8
10,200 –
10,000 –
9,800 –
9,600 –
9,400 –
9,200 –
9,000 –
| | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
Month
Inpatient Days
9911
9265
9764
9520
9691
9411
9949
9724
9542
9355
10068
9572

79. Adjusting Trend Data
Quarter I:
Quarter II:
Quarter III:
Quarter IV:

80. Associative Forecasting
Used when changes in one or more independent variables can be used to predict the changes in the dependent variable
Most common technique is linear regression analysis
We apply this technique just as we did in the time-series example

81. Associative Forecasting
Forecasting an outcome based on predictor variables using the least squares technique
y = a + bx ^
where y = value of the dependent variable (in our example, sales)
a = y-axis intercept
b = slope of the regression line
x = the independent variable ^

82. Associative Forecasting Example
NODEL’S SALES
(IN $ MILLIONS), y
AREA PAYROLL
(IN $ BILLIONS), x
2.0 1 2
3.0 3
2.5 4
3.5 7
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)

83. Associative Forecasting Example
SALES, y
PAYROLL, x x2 xy
2.0 1
3.0 3 9
9.0
2.5 4 16
10.0 2
4.0
3.5 7 49
24.5
Σy =
15.0
Σx = 18
Σx2 = 80
Σxy =
51.5

84. Associative Forecasting Example
SALES, y
PAYROLL, x x2 xy
2.0 1
3.0 3 9
9.0
2.5 4 16
10.0 2
4.0
3.5 7 49
24.5
Σy =
15.0
Σx = 18
Σx2 = 80
Σxy =
51.5

85. Associative Forecasting Example
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
SALES, y
PAYROLL, x x2 xy
2.0 1
3.0 3 9
9.0
2.5 4 16
10.0 2
4.0
3.5 7 49
24.5
Σy =
15.0
Σx = 18
Σx2 = 80
Σxy =
51.5

86. Associative Forecasting Example
If payroll next year is estimated to be $6 billion, then:
Sales (in $ millions) = (6)
= = 3.25
Sales = $3,250,000

87. Associative Forecasting Example
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
If payroll next year is estimated to be $6 billion, then:
3.25
Sales (in$ millions) = (6)
= = 3.25
Sales = $3,250,000

88. Standard Error of the Estimate
A forecast is just a point estimate of a future value
This point is actually the mean of a probability distribution
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
3.25
Regression line,
Figure 4.9

89. Standard Error of the Estimate
where y = y-value of each data point
yc = computed value of the dependent variable, from the regression equation
n = number of data points

90. Standard Error of the Estimate
Computationally, this equation is considerably easier to use
We use the standard error to set up prediction intervals around the point estimate

91. Standard Error of the Estimate
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
3.25
The standard error of the estimate is $306,000 in sales

92. Correlation
How strong is the linear relationship between the variables?
Correlation does not necessarily imply causality!
Coefficient of correlation, r, measures degree of association
Values range from -1 to +1

93. Correlation Coefficient

94. Correlation Coefficient
Figure 4.10 y x
(a) Perfect negative correlation y x
(e) Perfect positive correlation y x
(b) Negative correlation y x
(d) Positive correlation
High
Moderate
Low
Correlation coefficient values
| | | | | | | | |
–1.0 –0.8 –0.6 –0.4 – y x
(c) No correlation

95. Correlation Coefficienty x x2 xy y2
2.0 1
4.0
3.0 3 9
9.0
2.5 4 16
10.0
6.25 2
3.5 7 49
24.5
12.25
Σy =
15.0
Σx = 18
Σx2 = 80
Σxy =
51.5
Σy2 =
39.5

96. For the Nodel Construction example:
Correlation
Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x
Values range from 0 to 1
Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81

97. Multiple-Regression Analysis
If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables
Computationally, this is quite complex and generally done on the computer

98. Multiple-Regression Analysis
In the Nodel example, including interest rates in the model gives the new equation:
An improved correlation coefficient of r = .96 suggests this model does a better job of predicting the change in construction sales
Sales = (6) - 5.0(.12) = 3.00
Sales = $3,000,000

99. Monitoring and Controlling Forecasts
Tracking Signal
Measures how well the forecast is predicting actual values
Ratio of cumulative forecast errors to mean absolute deviation (MAD)
Good tracking signal has low values
If forecasts are continually high or low, the forecast has a bias error

100. Monitoring and Controlling Forecasts
Tracking signal
Cumulative error
MAD =

101. Tracking Signal Signal exceeding limit Tracking signal +
Figure 4.11
Tracking signal +
0 MADs –
Upper control limit
Lower control limit
Time
Signal exceeding limit
Acceptable range

102. Tracking Signal Example
QTR
ACTUAL DEMAND
FORECAST DEMAND
ERROR
CUM ERROR
ABSOLUTE FORECAST ERROR
CUM ABS FORECAST ERROR
MAD
TRACKING SIGNAL (CUM ERROR/MAD) 1 90
100
–10 10
10.0
–10/10 = –1 2 95 –5
–15 5 15
7.5
–15/7.5 = –2 3
115
+15 30
10.
0/10 = 0 4
110 40
10/10 = –1
125 +5 55
11.0
+5/11 = +0.5 6
140
+30
+35 85
14.2
+35/14.2 = +2.5
At the end of quarter 6,

103. Adaptive Smoothing
It’s possible to use the computer to continually monitor forecast error and adjust the values of the a and b coefficients used in exponential smoothing to continually minimize forecast error
This technique is called adaptive smoothing

104. Focus Forecasting
Developed at American Hardware Supply, based on two principles:
Sophisticated forecasting models are not always better than simple ones
There is no single technique that should be used for all products or services
Uses historical data to test multiple forecasting models for individual items
Forecasting model with the lowest error used to forecast the next demand

105. Forecasting in the Service Sector
Presents unusual challenges
Special need for short term records
Needs differ greatly as function of industry and product
Holidays and other calendar events
Unusual events

106. Fast Food Restaurant Forecast
20% –
15% –
10% –
5% –
(Lunchtime)
(Dinnertime)
Hour of day
Percentage of sales by hour of day
Figure 4.12

107. FedEx Call Center Forecast
12% –
10% –
8% –
6% –
4% –
2% –
0% –
Hour of day
A.M.
P.M. 2 4 6 8 10 12
Figure 4.12

108. Printed in the United States of America.
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Printed in the United States of America.